Transcript
®
Autodesk ™ Robot Structural Analysis Professional VERIFICATION MANUAL March 2014
according to: NAFEMS benchmarks: Linear Static Benchmarks vol. 1. (Ref: LSB 1) Selected Benchmarks for Forced Vibration (Ref: R0016) Background to FE Analysis of Geometric Non-linearity Benchmarks (Ref: R0065)
© 2014 Autodesk, Inc. All Rights Reserved. Except as otherwise permitted by Autodesk, Inc., this publication, or parts thereof, may not be reproduced in any form, by any method, for any purpose. Certain materials included in this publication are reprinted with the permission of the copyright holder. Disclaimer THIS PUBLICATION AND THE INFORMATION CONTAINED HEREIN IS MADE AVAILABLE BY AUTODESK, INC. “AS IS.” AUTODESK, INC. DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE REGARDING THESE MATERIALS. Trademarks The following are registered trademarks of Autodesk, Inc., in the USA and/or other countries: Autodesk Robot Structural Analysis Professional, Autodesk Concrete Building Structures, Spreadsheet Calculator, ATC, AutoCAD, Autodesk, Autodesk Inventor, Autodesk (logo), Buzzsaw, Design Web Format, DWF, ViewCube, SteeringWheels, and Autodesk Revit. All other brand names, product names or trademarks belong to their respective holders. Third Party Software Program Credits ACIS Copyright© 1989-2001 Spatial Corp. Portions Copyright© 2002 Autodesk, Inc. Copyright© 1997 Microsoft Corporation. All rights reserved. International CorrectSpell™ Spelling Correction System© 1995 by Lernout & Hauspie Speech Products, N.V. All rights reserved. InstallShield™ 3.0. Copyright© 1997 InstallShield Software Corporation. All rights reserved. PANTONE® and other Pantone, Inc. trademarks are the property of Pantone, Inc.© Pantone, Inc., 2002. Portions Copyright© 1991-1996 Arthur D. Applegate. All rights reserved. Portions relating to JPEG © Copyright 1991-1998 Thomas G. Lane. All rights reserved. Portions of this software are based on the work of the Independent JPEG Group. Portions relating to TIFF © Copyright 1997-1998 Sam Leffler. © Copyright 1991-1997 Silicon Graphics, Inc. All rights reserved. Government Use Use, duplication, or disclosure by the U.S. Government is subject to restrictions as set forth in FAR 12.212 (Commercial Computer Software-Restricted Rights) and DFAR 227.7202 (Rights in Technical Data and Computer Software), as applicable.
Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Table of contents INTRODUCTION .......................................................................................................................................................... 1 SHELL LINEAR STATIC ANALYSIS ................................................................................................................................ 2 TEST IC1 - tapered membrane end load ........................................................................................................ 3 TEST IC2 - tapered membrane gravity loading .............................................................................................. 4 TEST IC3 - tapered membrane edge shear.................................................................................................... 5 TEST IC4 - tapered cantilever gravity load ..................................................................................................... 6 TEST IC10 - tapered plate edge shear ........................................................................................................... 7 TEST IC11 - tapered plate gravity load ........................................................................................................... 8 TEST IC13 - skew plate normal pressure ....................................................................................................... 9 TEST IC29 - Z-section cantilever torsion bending .........................................................................................10 TEST IC30 - Z-section cantilever beam bending...........................................................................................11 DYNAMIC ANALYSIS ................................................................................................................................................12 TESTS No 5 - Vibrations of a Deep Beam.....................................................................................................13 Results of Modal Analysis (5)..........................................................................................................................13 Results of Harmonic Forced Vibration (5H) ...................................................................................................14 Results of Periodic Forced Vibration (5P) ......................................................................................................14 Results of Impulse Forced Vibration (5T).......................................................................................................14 TESTS No 13 - Vibrations of Simply Supported Thin Plate ..........................................................................15 Results of Modal Analysis (13) .......................................................................................................................16 Results of Harmonic Forced Vibration (13H) .................................................................................................17 Results of Periodic Forced Vibration (13P) ....................................................................................................17 Results of Impulse Forced Vibration (13T) ....................................................................................................18 TESTS No 21 - Vibrations of Simply Supported Thick Plate ........................................................................19 Results of Modal Analysis (21) .......................................................................................................................20 Results of Harmonic Forced Vibration (21H) .................................................................................................21 Results of Periodic Forced Vibration (21P) ....................................................................................................21 Results of Impulse Forced Vibration (21T) ....................................................................................................22 LARGE ROTATIONS AND DISPLACEMENTS ...............................................................................................................23 TEST GNL-5 – Large rotations and displacements of a straight cantilever ................................................24 CONCLUSIONS ...........................................................................................................................................................26
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
INTRODUCTION This report contains a range of static and dynamic benchmark tests covering a few types of behaviour encountered in structural analysis. These examples have been taken from: "Linear Static Benchmarks vol.1" signed by NAFEMS as LSB1, “Selected Benchmarks for Forced Vibration” signed by NAFEMS as R0016; “Background to FE Analysis of Geometric Non-linearity Benchmarks” signed by NAFEMS as R0065. Benchmark results (signed as “NAFEMS”) were recalled, and originally compared with results of Autodesk Robot Structural Analysis Professional version 2013 (signed further as “Robot”). The comparison of results is still valid for the next versions. Each problem contains the following parts: - the name of the benchmark as used in NAFEMS manual, - short problem description, - scheme of the model, - comparison between Robot results and reference values.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
SHELL LINEAR STATIC ANALYSIS
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC1 - tapered membrane end load Name of the test: Reference: Specification: GEOMETRY:
IC1 NAFEMS LSB1 Linear static analysis of an elastic membrane.
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary conditions: Material properties: Element type: DATA FILE:
Uniformly distributed horizontal load of 10 MN/m (pressure of 100 Mpa) along outer edge. Nodes on X=0.0 – blocked UX, UZ, RY, node (0.0, 2.0) - fully clamped. Isotropic, E=210e3 MPa, ni=0.3 Shell 8-node quadrilaterals Nafems_IC01.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
NAFEMS 61.9 60.9 61.3 -----
Direct stress sxx at point no. 8 (0.0, 2.0) Robot Difference 65.38 6.66% 61.79 0.80% 61.53 0.38% 61.39 0.15% 61.35 0.08%
61.3 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC2 - tapered membrane gravity loading Name of the test: Reference: Specification: GEOMETRY:
IC2 NAFEMS LSB1 Linear static analysis of an elastic membrane.
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary conditions: Material properties: Element type: DATA FILE:
Uniform acceleration 9.81 m/s2 in global X direction (gravity). Nodes on X=0.0 – blocked UX, UZ, RY, node (0.0, 2.0) - fully clamped. Isotropic, E=210e3 MPa, ni=0.3, p=7 MG/m3 Shell 8-node quadrilaterals Nafems_IC02.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
NAFEMS 0.258 0.247 0.247 -----
Direct stress sxx at point no. 8 (0.0, 2.0) Robot Difference 0.2697 9.19% 0.2487 0.69% 0.2477 0.28% 0.2471 0.04% 0.2469 0.04%
0.247 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC3 - tapered membrane edge shear Name of the test: Reference: Specification: GEOMETRY:
IC3 NAFEMS LSB1 Linear static analysis of an elastic membrane.
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
Uniform surface shear traction of 100 Mpa in the vertical Y- direction. Edge X=0.0 – fully fixed. Isotropic, E=210e3 MPa, ni=0.3 Shell 8-node quadrilaterals Nafems_IC03.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
NAFEMS 28.7 27.9 27.3 -----
Direct stress sxy at point no. 8 (0.0, 2.0) Robot Difference 26.889 0.04% 27.166 0.99% 27.157 0.96% 26.945 0.17% 26.862 0.14%
26.9 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC4 - tapered cantilever gravity load Name of the test: Reference: Specification: GEOMETRY:
IC4 NAFEMS LSB1 Linear static analysis of an elastic plate
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
Uniform acceleration 9.81 m/s2 in the vertical Y direction (gravity). Edge X=0.0 – fully fixed. Isotropic, E=210e3 MPa, ni=0.3, p=7 MG/m3 shell 8-node quadrilaterals Nafems_IC04.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
NAFEMS 0.198 0.200 0.200 -----
Direct stress sxy at point no. 8 (0.0, 2.0) Robot Difference 0.1831 8.45% 0.2000 0.00% 0.1992 0.40% 0.1990 0.50% 0.1991 0.45%
0.2000 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC10 - tapered plate edge shear Name of the test: Reference: Specification: GEOMETRY:
IC10 NAFEMS LSB1 Linear static analysis of an elastic plate
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
Uniform vertical shear 10 kN/m in the Z direction along outer edge. Edge X=0.0 – fully fixed. Isotropic, E=210e3 MPa, ni=0.3 shell 8-node quadrilaterals Nafems_IC10.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
Value of Direct stress sxx on top surface at point no 8 (0.0, 2.0) NAFEMS Robot Difference 14.3 14.750 0.34% 14.5 14.684 0.11% 14.6 14.610 0.61% --14.626 0.50% --14.630 0.48%
14.7 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC11 - tapered plate gravity load Name of the test: Reference: Specification: GEOMETRY:
IC11 NAFEMS LSB1 Linear static analysis of an elastic plate
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
Uniform acceleration 9.81 m/s2 in the vertical Z direction (gravity). Edge X=0.0 – fully fixed. Isotropic, E=210e3 MPa, ni=0.3 shell 8-node quadrilaterals Nafems_IC11.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
Value of Direct stress sxx on top surface at point no 8 (0.0, 2.0) NAFEMS Robot Difference 24.0 24.506 5.75% 25.5 25.675 1.25% 25.7 25.748 0.97% --25.830 0.65% --25.851 0.57%
26 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC13 - skew plate normal pressure Name of the test: Reference: Specification: GEOMETRY:
IC13 NAFEMS LSB1 Linear static analysis of an elastic plate
Thickness = 0.01 m
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
Normal pressure –0.7 kPa in the vertical Z direction. Simple supports ( no z-displacement) for all edges. Isotropic, E=210e3 MPa, ni=0.3 shell 8-node quadrilaterals Nafems_IC13.rtd
RESULTS COMPARISON:
Mesh refinement 2x2 4x4 8x8 16x16 32x32 TARGET:
March 2014
Maximum principal stress on the lower surface at the plate center NAFEMS Robot Difference 0.757 0.5253 34.50 % 0.795 0.7214 10.04 % --0.7163 10.68 % --0.7678 4.26 % --0.7998 0.27 %
0.802 MPa
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC29 - Z-section cantilever torsion bending Name of the test: Reference: Specification: GEOMETRY:
IC29 NAFEMS LSB1 Linear static analysis of an elastic shell
Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
Torque of 1.2 MNm at end x=10, by two uniformly distributes edge shears, S=0.6 MN at each flange. At edge x=0 all displacements are zero. Isotropic, E=210e3 MPa, ni=0.3 Shell 8-node quadrilaterals Nafems_IC29.rtd
RESULTS COMPARISON:
Point 1 2 3 4 5 6 7
March 2014
Direct stress sxx at mid surface at points in ¼ of the beam’s length Target NAFEMS Robot Difference -108.8 -110.1 -110.10 1.19% -36.26 -36.9 -36.88 1.71% 36.26 36.2 36.04 0.61% 36.26 37.3 37.72 4.03% 36.26 36.2 36.04 0.61% -36.26 -36.9 -36.88 1.71% -108.8 -110.1 -110.10 1.19%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST IC30 - Z-section cantilever beam bending Name of the test: Reference: Specification: GEOMETRY:
IC30 NAFEMS LSB1 Linear static analysis of an elastic shell Thickness = 0.1 m
DATA DEFINITION: Loading: Boundary condition:
Material properties: Element type: DATA FILE:
Shear force S=0.6 MN as a uniformly distributed edge shear on the central web. At edge x=0 all x-displacements are zero. y-displacements are zero at the origin, z-displacements are zero at the corners of the two flanges at (0,-1,-1) and (0,1,1) Isotropic, E=210e3 MPa, ni=0.3 Shell 8-node quadrilaterals Nafems_IC30.rtd
RESULTS COMPARISON:
Point 1 2 3 4 5 6 7
March 2014
Direct stress sxx at mid surface at points in ¼ of the beam’s length Target NAFEMS Robot Difference 193.0 191.0 194.48 0.77% -96.5 -96.7 -97.25 0.78% -386.0 -383.0 -386.22 0.06% 0.0 0.0 0.0 0.00% 386.0 383.0 386.22 0.06% 96.5 96.7 97.25 0.78% -193.0 -191.0 -194.48 0.77%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
DYNAMIC ANALYSIS
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TESTS No 5 - Vibrations of a Deep Beam Name of the test: Reference: Specification: GEOMETRY:
DATA DEFINITION: Loading: Boundary condition: Material properties: Element type: DATA FILE:
5, 5H, 5P, 5T NAFEMS R0016 Dynamic analysis of an elastic beam Length: L = 10 m Section: a = b = 2 m
Uniform load Fo=106 [N/m] (Fo=1000 [kN/m]) X=Y=Z=RX=0 (at the beginning of the beam) Y=Z=0 (at the end of the beam) E=200x109 N/m2 ; =0,3 ; =8000 kg/m3 10 beam elements, using attribute: „Consider shear forces in deformation calculation‟ (Timoshenko‟s Beam – deep beam). Nafems_05.rtd
RESULTS COMPARISON:
Results of Modal Analysis (5) OUTPUT: Frequencies [Hz]
Modes 1&2 3 4 5&6 7 8&9
March 2014
NAFEMS 42.65 71.20 125.00 148.15 213.61 283.47
Robot 42.49 71.26 125.11 143.79 215.54 259.36
Difference 0.38% 0.08% 0.09% 3.15% 0.90% 8.51%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Harmonic Forced Vibration (5H) Forcing function: F=Fosin(2ft) OUTPUT:
Peak Displacement [mm] Peak Stress [MPa] Note: Response at the middle node of the beam (node no 7) for the 1st mode frequency f=42.49[Hz]
NAFEMS 13.45
Peak Displacement [mm] Difference Robot 13.43
0.15%
NAFEMS
Peak Stress [MPa] Robot
Difference
241.9
242.4
0.21%
Results of Periodic Forced Vibration (5P) Forcing function: F=Fo[sin(2ft)-sin(3(2ft))] OUTPUT:
Peak Displacement [mm] Peak Stress [MPa] Note: Response at the middle node of the beam (node no 7) for the frequency f=20[Hz]
NAFEMS 0.951
Peak Displacement [mm] Difference Robot 0.954
0.32%
NAFEMS
Peak Stress [MPa] Robot
Difference
17.10
17.36
1.52%
Results of Impulse Forced Vibration (5T) Forcing function: F=Fo OUTPUT:
Peak Displacement [mm] and the corresponding Time [s] Peak Stress [MPa] Static Displacement [mm] Note: Response at the middle node of the beam (node no 7)
NAFEMS
Peak Displacement [mm] Difference Robot
NAFEMS
at the Time [s] Robot
Difference
0.0117
0.0%
1.043
1.047
0.38%
0.0117
NAFEMS
Peak Stress [MPa] Robot
Difference
NAFEMS
18.76
18.72
0.21%
0.538
March 2014
Static Displacement [mm] Difference Robot 0.537
0.19%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TESTS No 13 - Vibrations of Simply Supported Thin Plate Name of the test: Reference: Specification: GEOMETRY:
DATA DEFINITION: Loading: Boundary condition:
Material properties: Element type:
13, 13H, 13P, 13T NAFEMS R0016 Dynamic analysis of an elastic plate Length: A = B = 10 m Thickness: t = 0,05 m
Uniform planar load Fo=100 [N/m 2] (Fo=0,1 [kN/m2]) X=Y=RZ=0 (at all nodes - Plate) Z=0 (at all edges) RX=0 (along edges X=0 & X=10 m) RY=0 (along edges Y=0 & Y=10 m) E=200x109 N/m2 ; =0,3 ; =8000 kg/m3 4-node quadrilateral shell elements (three models of mesh considered: 4x4, 8x8, and 16x16 elements).
RESULTS COMPARISON:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Modal Analysis (13) OUTPUT: Frequencies [Hz]
Modes
NAFEMS
1 2&3 4 5&6 7&8
2.377 5.942 9.507 11.884 15.449
Modes
NAFEMS
1 2&3 4 5&6 7&8
2.377 5.942 9.507 11.884 15.449
Modes
NAFEMS
1 2&3 4 5&6 7&8
2.377 5.942 9.507 11.884 15.449
March 2014
Robot (meshing 4x4) 2.512 7.071 11.738 16.559 21.311
Robot (meshing 8x8) 2.410 6.216 10.047 13.201 17.073
Robot (meshing 16x16) 2.385 6.009 9.638 12.201 15.840
Difference 5.68% 19.00% 23.47% 39.34% 37.94%
Difference 1.39% 4.61% 5.68% 11.08% 10.51%
Difference 0.34% 1.13% 1.38% 2.67% 2.53%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Harmonic Forced Vibration (13H) Forcing function: F=Fosin(2ft) OUTPUT:
Peak Displacement [mm] Peak Stress [MPa]
Note: Response at the centre of the plate (node no 1) for the 1st mode frequency f=2.512[Hz] (4x4); f=2.410[Hz] (8x8); f=2.385[Hz] (16x16)
Meshing
Peak Displacement [mm] NAFEMS Robot Difference
NAFEMS
Peak Stress [MPa] Robot
Difference
4x4
45.42
44.66
1.67%
30.03
33.20
10.56%
8x8
45.42
45.11
0.68%
30.03
32.23
7.33%
16x16
45.42
45.11
0.68%
30.03
31.90
6.23%
NAFEMS
Peak Stress [MPa] Robot
Difference
Results of Periodic Forced Vibration (13P) Forcing function: F=Fo[sin(2ft)-sin(3(2ft))] OUTPUT:
Peak Displacement [mm] Peak Stress [MPa]
Note: Response at the centre of the plate (node no 1) for frequency f=1.2[Hz]
Meshing
Peak Displacement [mm] NAFEMS Robot Difference
4x4
2.863
3.070
7.23%
2.018
2.322
15.06%
8x8
2.863
2.915
1.82%
2.018
2.118
4.96%
16x16
2.863
2.884
0.73%
2.018
2.076
2.87%
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Impulse Forced Vibration (13T) Forcing function: F=Fo OUTPUT:
Peak Displacement [mm] and the corresponding Time [s] Peak Stress [MPa] Static Displacement [mm]
Note: Response at the centre of the plate (node no 1)
Meshing
Peak Displacement [mm] NAFEMS Robot Difference
NAFEMS
at the Time [s] Robot
Difference
4x4
3.523
3.447
2.16%
0.210
0.200
4.76%
8x8
3.523
3.479
1.25%
0.210
0.210
0.0%
16x16
3.523
3.448
2.13%
0.210
0.210
0.0%
NAFEMS
Peak Stress [MPa] Robot
Difference
4x4
2.484
2.322
6.52%
1.817
1.767
2.75%
8x8
2.484
2.462
0.86%
1.817
1.774
2.37%
16x16
2.484
2.361
4.95%
1.817
1.775
2.31%
Meshing
March 2014
Static Displacement [mm] NAFEMS Robot Difference
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TESTS No 21 - Vibrations of Simply Supported Thick Plate Name of the test: Reference: Specification: GEOMETRY:
DATA DEFINITION: Loading: Boundary condition:
Material properties: Element type:
21, 21H, 21P, 21T NAFEMS R0016 Dynamic analysis of an elastic plate Length: A = B = 10 m Thickness: t = 1,0 m
Uniform planar load Fo=106 [N/m2] (Fo=1000 [kN/m 2]) X=Y=RZ=0 (at all nodes - Plate) Z=0 (at all edges) RX=0 (along edges X=0 & X=10 m) RY=0 (along edges Y=0 & Y=10 m) E=200x109 N/m2 ; =0,3 ; =8000 kg/m3 4-node quadrilateral shell elements (three models of mesh considered: 4x4, 8x8, and 16x16 elements).
RESULTS COMPARISON:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Modal Analysis (21) OUTPUT: Frequencies [Hz]
Modes
NAFEMS
1 2&3 4 5&6 7&8
45.897 109.44 167.89 204.51 256.50
Modes
NAFEMS
1 2&3 4 5&6 7&8
45.897 109.44 167.89 204.51 256.50
Modes
NAFEMS
1 2&3 4 5&6 7&8
45.897 109.44 167.89 204.51 256.50
March 2014
Robot (meshing 4x4) 48.589 129.99 207.34 280.29 350.94
Robot (meshing 8x8) 46.542 114.67 178.12 226.35 283.72
Robot (meshing 16x16) 46.065 110.94 170.89 210.56 264.31
Difference 5.87% 18.78% 23.50% 37.05% 36.82%
Difference 1.41% 4.78% 6.09% 10.68% 10.61%
Difference 0.37% 1.37% 1.79% 2.96% 3.04%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Harmonic Forced Vibration (21H) Forcing function: F=Fosin(2ft) OUTPUT:
Peak Displacement [mm] Peak Stress [MPa] st
Note: Response at the centre of the plate (node no 1) for the 1 mode frequency f=48.589[Hz] (4x4); f=46.542[Hz] (8x8); f=46.065[Hz] (16x16)
Meshing
Peak Displacement [mm] NAFEMS Robot Difference
NAFEMS
Peak Stress [MPa] Robot
Difference
4x4
58.33
58.93
1.03%
800.8
866.9
8.25%
8x8
58.33
59.64
2.25%
800.8
825.6
3.10%
16x16
58.33
59.71
2.37%
800.8
807.6
0.85%
NAFEMS
Peak Stress [MPa] Robot
Difference
Results of Periodic Forced Vibration (21P) Forcing function: F=Fo[sin(2ft)-sin(3(2ft))] OUTPUT:
Peak Displacement [mm] Peak Stress [MPa]
Note: Response at the centre of the plate (node no 1) for frequency f=20[Hz]
Meshing
Peak Displacement [mm] NAFEMS Robot Difference
4x4
4.929
6.127
24.31%
67.67
91.19
34.76%
8x8
4.929
5.328
8.09%
67.67
75.23
11.17%
16x16
4.929
5.175
4.99%
67.67
71.40
5.51%
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Results of Impulse Forced Vibration (21T) Forcing function: F=Fo OUTPUT:
Peak Displacement [mm] and the corresponding Time [s] Peak Stress [MPa] Static Displacement [mm]
Note: Response at the centre of the plate (node no 1)
Meshing
Peak Displacement [mm] NAFEMS Robot Difference
NAFEMS
at the Time [s] Robot
Difference
4x4
4.524
4.563
0.86%
0.0108
0.0104
3.7%
8x8
4.524
4.528
0.09%
0.0108
0.0105
2.78%
16x16
4.524
4.578
1.19%
0.0108
0.0105
2.78%
NAFEMS
Peak Stress [MPa] Robot
Difference
4x4
62.11
66.32
6.78%
2.333
2.317
0.69%
8x8
62.11
59.86
3.62%
2.333
2.323
0.43%
16x16
62.11
60.25
2.99%
2.333
2.322
0.47%
Meshing
March 2014
Static Displacement [mm] NAFEMS Robot Difference
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
LARGE ROTATIONS AND DISPLACEMENTS
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
VERIFICATION EXAMPLE TEST GNL-5 – Large rotations and displacements of a straight cantilever Name of the test: Reference: Specification: GEOMETRY:
DATA DEFINITION: Loading: Boundary condition: Material properties: Discretization:
GNL-5 NAFEMS R0065 Geometric nonlinearity Length: Cross section:
3,2 m rectangular 0,1x0,1 m
Concentrated moment at the end point M = 3 436,1 [kN*m] (applied in 36 equal increments) Built-in at the begin E=210x109 N/m2 ; =0,0 (density not considered) 8 beam elements, 40 load increments, analysis P-delta, nonlinear.
RESULTS COMPARISON:
“Dimensionless” value of tip displacements and rotations (UX=100*ux/L, UY=100*uy/L, RZ=100*rz/2*) are presented on the analytical plot, and summarized in the table, below.
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
Normalized horizontal displacement at tip versus normalized bending moment M/Mmax 0,2 0,4 0,6 0,8 1,0
analyt. 24,3 76,6 115,6 118,9 100,0
Robot 24,3 76,5 115,8 119,3 100,0
diff -0,3% -0,1% 0,1% 0,3% 0,0%
Normalized vertical displacement at tip versus normalized bending moment M/Mmax 55,0 72,0 48,0 13,7 0,0
analyt. 55,0 72,0 48,0 13,7 0,0
Robot 55,0 72,3 48,4 14,0 0,0
diff 0,1% 0,4% 0,9% 1,6% 0,0%
Normalized rotations at tip versus normalized bending moment M/Mmax 0,0 0,0 0,0 0,0 0,0
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analyt. 20,0 40,0 60,0 80,0 100,0
Robot 20,0 40,0 60,0 80,0 100,0
diff 0,0% 0,0% 0,0% 0,0% 0,0%
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Autodesk Robot Structural Analysis Professional - Verification Manual NAFEMS benchmarks
CONCLUSIONS The results and accuracy achieved in verification examples confirm the quality and reliability of Robot. This state-of-the-art structural analysis and design software gives sufficient accuracy limited only by the precision of modeling.
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